This is a proposal to develop and evaluate statistical methods for clinical trials where "equivalence" of the treatments is, or is part of, the study hypothesis. Such trials arise in drug development where a new formulation of an existing product must demonstrate equivalent bioavailability to the existing product. These "bioequivalence" trials are the basis for approving generic drugs. Equivalence trials also can compare direct therapeutic outcomes (clinical equivalence). Clinical equivalence trials arise, for example, in evaluating therapies that need not be superior in the primary clinical endpoint in order to be preferable to existing practice. Such trials are appropriate, for example, if the new therapy has a better side-effect profile. In a general sense, we seek to fill the voids in statistical methods for equivalence trials, both interval equivalence and one-tailed, and for both bioequivalence and clinical equivalence applications. More specifically, we will develop and evaluate parametric and nonparametric methods for equivalence of distributions and methods for equivalence of time profiles, calculate sample size tables and/or graphs for use by researchers in the applied fields, and develop procedures so that methods we develop can be used with early stopping rules.